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Honors Immediate Algebra

CATALOG DESCRIPTION

Brief Course Description


Honors Intermediate Algebra builds on the material from Honors Beginning Algebra.
The course begins with a review of the real number system and solutions of linear
equations and inequalities . Students learn to solve equations and inequalities involving
absolute value. Following this, graphs of linear equations are reviewed and students
learn additional material about functions and variation. After a review of solutions to 2x2
systems, students learn how to solve 3x3 and 4x4 systems of linear equations.
Operations on polynomials , including factoring , are covered, along with rational
expressions. Radical expressions are reviewed , and students learn to solve equations
involving several radical expressions. Students learn to apply the quadratic formula to
equations that are quadratic in type, and they investigate solutions to quadratic and
rational inequalities. Beginning with a general study of inverse functions, students learn
the basic properties of exponential and logarithmic functions and apply them to realworld
problems. Finally, the course concludes with an introduction to arithmetic series,
geometric series, and the binomial theorem.

Pre-Requisites: Required: Honors Beginning Algebra

TEXTS AND SUPPLEMENTAL INSTRUCTIONAL MATERIALS


Supplemental Instructional Materials (please describe)

Education Program for Gifted Youth (EPGY) Intermediate Algebra course. EPGY offers
students mathematics courses by presenting the material on personal computers, in a
way that aims to replicate the classroom environment as closely as possible. Students
complete lessons which include multimedia lectures, online exercises, and derivations.
Derivation exercises ask students to justify their steps in an interactive workshop
environment.

COURSE CONTENT

A. Course Purpose.


Honors Intermediate Algebra requires that students master the following specific topics:
• Algebraic Expressions
• The Real Number System, The Order of Operations , Properties of Real Number
Linear Equations and Inequalities
• Linear Equations and Inequalities, Absolute Value Equations and Inequalities,
Graphing
• Linear Equations, Relations, Functions, Variation
• Systems of Linear Equations
• Solving 2x2, 3x3 and 4x4 Systems of Equations with Applications
• Polynomial Functions
• operations on Polynomials, Polynomial Long Division, Factoring, Special
Factorizations,
• Solving Equations by Factoring, Applications
• Rational Functions
• Operations on Rational Expressions, Graphing Rational Functions, Applications
Radical Functions
• Operations on Radical Expressions, Graphing Radical Expressions, Complex
Numbers, Applications
• Exponential and Logarithmic Functions
• Inverse Functions, Exponential Functions, Exponential Equations, Logarithmic
• Functions, Evaluating Logarithms, Logarithmic Equations, Exponential Growth and
Decay, The Change-of-base Formula

B. Course Outline. Detailed description of topics covered. Show examples of how the
text or readings are incorporated into the topics covered.

Lesson Number Concepts Covered

Textbook Section
• Sets; real numbers; order of operations; properties of real number
• Linear equations and inequalities in one variable; applications
• Absolute value; equations involving absolute value; applications
• Set operations; interval notation; solving compound inequalities
• Solving absolute value inequalities; applications
• Slope and the equation of a line; 2x2 systems of linear equations
• Systems of linear inequalities in two variables ; variation
• Solving 2x2 systems of linear equations
• Solving 3x3 and 4x4 systems of linear equations; applications
• Relations and functions; domain and range; vertical line test
• Linear functions; operations on functions; composition of functions
• Identifying linear, quadratic, polynomial, and square root functions
• Polynomial functions; adding, subtracting, and multiplying polynomials
• Factoring: by grouping , trinomials, special factorizations
• Adding, subtracting, multiplying, and dividing rational expressions
• Rational Expressions and Functions
• Appendix C Polynomial long division; synthetic division
• Graphing rational functions; applications: proportions, work, distance-rate-time
• Adding, subtracting, multiplying, and dividing radical expressions; graphs
• Solving equations involving radical expressions; complex numbers
• Solving quadratic equations: completing the square and the quadratic formula
• The discriminant; use of the discriminant to analyze quadratic equations
• Solving equations quadratic in form; applications: area, quadratic functions, etc.
• Solving quadratic and rational inequalities
• Inverse functions; horizontal line test; finding the inverse of a function
• Exponential functions; solving exponential equations; exponential growth/decay
• Logarithmic functions; graphs; solving logarithmic equations
• Properties of logarithms; simplifying logarithmic expressions
Common logarithms ; natural logarithms
• Exponential and logarithmic equations; compound interest, exponential growth
• The change-of-base formula
• Sequences and series; finding general terms; evaluating series
• Sigma notation
• Arithmetic sequences; general term; finite sums of arithmetic sequences
• Geometric sequences; general term; finite/infinite sums of geometric sequences
• The Binomial Theorem; Pascal’s triangle; finding terms of binomial expansions
• Additional Graphs of Functions
• The Circle and the Ellipse
• The Hyperbola and Functions defined by Radicals
• Nonlinear Systems of Equations
• Second-Degree Inequalities and Systems of Inequalitites

B. Key Assignments:

Homework - The homework assignments are picked from the textbook and submitted to
the instructor. The homework assignments are used as a tool for reinforcing the material
presented and discussed in class.

Software lessons and quizzes - The software lessons further the students
understanding and depths of the material. The software EPGY offers presents the
material on personal computers, in a way that aims to replicate the classroom
environment as closely as possible. Students complete lessons which include
multimedia lectures, online exercises, and derivations. Derivation exercises ask
students to justify their steps in an interactive workshop environment.The software is
interactive and gives students feedback on problems they missed. The student's work is
sent through the software and processed by the Stanford servers.

Chapter Exams - The students take chapter exams in the course software.

Midterm and Final Exams - The students take comprehensive proctored midterm and
final exams during the course of the semester.

D. Instructional Methods and/or Strategies

The classroom time is used to present new information, discuss homework assignments
that students had difficulty with, and present more challenging problems. The EPGY
software is used as a tool to enhance student understanding of the material. In the
software, students complete lessons which include multimedia lectures, online
exercises, and derivations. Derivation exercises ask students to justify their steps in an
interactive workshop environment. The software gives students feedback on the
problems they missed.

E. Assessment Methods and/or Tools

The assessments tools include: EPGY software lessons, quizzes, chapter exams,
proctored comprehensive midterm exams, and a proctored comprehensive final exam.

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